Calculate the ratio of the magnitude of the electric force to the gravitational force exerted between two protons.

Step-by-step solution

The electric force between two protons separated by a distance r is given by Coulomb's law: F_ e = 1 4 ₀ e^2 r^2 The gravitational force between them is given by Newton's law of gravitation: F_ g = G m_ p ^2 r^2 The ratio of the electric force to the gravitational force is: F_ e F_ g = e^2 4 ₀ G m_ p ^2 Substituting the standard values: e = 1.6 10⁻¹⁹ C 1 4 ₀ = 9 10^9 N m ^2 /C ^2 G = 6.67 10⁻¹¹ N m ^2 /kg ^2 m_ p = 1.67 10⁻²⁷ kg F_ e F_ g = 9 10^9 (1.6 10⁻¹⁹)^2 6.67 10⁻¹¹ (1.67 10⁻²⁷)^2 F_ e F_ g = 9 10^9 2.56 10⁻³